{"id":"https://openalex.org/W1601605622","doi":"https://doi.org/10.1007/3-540-60217-8_19","title":"On lower bounds for the depth of threshold circuits with weights from {\u22121,0,+1}","display_name":"On lower bounds for the depth of threshold circuits with weights from {\u22121,0,+1}","publication_year":1995,"publication_date":"1995-01-01","ids":{"openalex":"https://openalex.org/W1601605622","doi":"https://doi.org/10.1007/3-540-60217-8_19","mag":"1601605622"},"language":"en","primary_location":{"id":"doi:10.1007/3-540-60217-8_19","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-60217-8_19","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5029149047","display_name":"Andreas Albrecht","orcid":"https://orcid.org/0000-0002-9813-4319"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Andreas Albrecht","raw_affiliation_strings":["BerCom GmbH, Bruno-Taut-Str. 4-6, D-12524, Berlin, Germany","BerCom GmbH"],"affiliations":[{"raw_affiliation_string":"BerCom GmbH, Bruno-Taut-Str. 4-6, D-12524, Berlin, Germany","institution_ids":[]},{"raw_affiliation_string":"BerCom GmbH","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5029149047"],"corresponding_institution_ids":[],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.18846636,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"404","last_page":"416"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12072","display_name":"Machine Learning and Algorithms","score":0.9944999814033508,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/bounded-function","display_name":"Bounded function","score":0.7016032934188843},{"id":"https://openalex.org/keywords/boolean-function","display_name":"Boolean function","score":0.6933709383010864},{"id":"https://openalex.org/keywords/boolean-circuit","display_name":"Boolean circuit","score":0.6810406446456909},{"id":"https://openalex.org/keywords/electronic-circuit","display_name":"Electronic circuit","score":0.6597608327865601},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.6447588801383972},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.5954810380935669},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5258370637893677},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.48532193899154663},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.47755369544029236},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4656311869621277},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4267197847366333},{"id":"https://openalex.org/keywords/parity-function","display_name":"Parity function","score":0.4139418601989746},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4012224078178406},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39179563522338867},{"id":"https://openalex.org/keywords/boolean-expression","display_name":"Boolean expression","score":0.39051035046577454},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.3330484628677368},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.28248700499534607},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.2245592176914215},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.08730065822601318},{"id":"https://openalex.org/keywords/electrical-engineering","display_name":"Electrical engineering","score":0.07475706934928894}],"concepts":[{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.7016032934188843},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.6933709383010864},{"id":"https://openalex.org/C141796577","wikidata":"https://www.wikidata.org/wiki/Q837479","display_name":"Boolean circuit","level":3,"score":0.6810406446456909},{"id":"https://openalex.org/C134146338","wikidata":"https://www.wikidata.org/wiki/Q1815901","display_name":"Electronic circuit","level":2,"score":0.6597608327865601},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.6447588801383972},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.5954810380935669},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5258370637893677},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.48532193899154663},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.47755369544029236},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4656311869621277},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4267197847366333},{"id":"https://openalex.org/C188183281","wikidata":"https://www.wikidata.org/wiki/Q2898309","display_name":"Parity function","level":4,"score":0.4139418601989746},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4012224078178406},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39179563522338867},{"id":"https://openalex.org/C158465420","wikidata":"https://www.wikidata.org/wiki/Q1979515","display_name":"Boolean expression","level":3,"score":0.39051035046577454},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.3330484628677368},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.28248700499534607},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2245592176914215},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08730065822601318},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.07475706934928894},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/3-540-60217-8_19","is_oa":false,"landing_page_url":"https://doi.org/10.1007/3-540-60217-8_19","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W36665231","https://openalex.org/W1589293917","https://openalex.org/W1649899421","https://openalex.org/W1846794677","https://openalex.org/W1990284858","https://openalex.org/W2010465749","https://openalex.org/W2014593388","https://openalex.org/W2014850486","https://openalex.org/W2015950107","https://openalex.org/W2047430378","https://openalex.org/W2069864904","https://openalex.org/W2070678975","https://openalex.org/W2097512637","https://openalex.org/W2097575812","https://openalex.org/W2097886040","https://openalex.org/W2114527013","https://openalex.org/W2116794057","https://openalex.org/W2117508909","https://openalex.org/W2165293955","https://openalex.org/W2169974244","https://openalex.org/W2912133662","https://openalex.org/W4233039852"],"related_works":["https://openalex.org/W1597080238","https://openalex.org/W2106622045","https://openalex.org/W2055594799","https://openalex.org/W3204916073","https://openalex.org/W2516690985","https://openalex.org/W2062972911","https://openalex.org/W2611822924","https://openalex.org/W1564702418","https://openalex.org/W2011175857","https://openalex.org/W2728195892"],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}